A rectangle has an area 30 cm2 and perimeter 26 cm. Its sides (in cm) are
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Correct Answer: Option A
Detailed Explanation:
Let length = l cm and breadth = b cm.
Area equation: l × b = 30
Perimeter equation: 2(l + b) = 26 ⇒ l + b = 13
From l + b = 13, we get b = 13 - l. Substituting in l × b = 30:
l(13 - l) = 30 ⇒ 13l - l² = 30 ⇒ l² - 13l + 30 = 0
Factoring: (l - 10)(l - 3) = 0 ⇒ l = 10 or l = 3
If l = 10, then b = 3; if l = 3, then b = 10.
The sides are 10 cm and 3 cm.
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The lengths of the diagonals of a rhombus are 10 cm and 24 cm. Its perimeter is
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